The former England captain hung up his boots at the end of the 2012/13 campaign - bringing a distinguished career to a close.
A man who turned out for Manchester United, Real Madrid and LA Galaxy brought the curtain down with French giants Paris St Germain.
His focus has now switched to other areas, with Beckham hoping to take a new MLS franchise to Miami.
Bolivar, though, have expressed an interest in adding the 38-year-old to their ranks for a one-off performance.
Marketing director Salomon Chalan told Globo Esporte: "Yes, that's true, we want Beckham to play one game for Bolivar.
"Talks are at an early stage between (owner of the company which runs Bolivar) Marcelo Claure and David Beckham, who are friends.
"I don't know yet if it will be a Libertadores game or a friendly one, they are talking and it is a complicated subject."
While Chalan is optimistic regarding the possibility of putting a deal in place, Bolivar president Guido Loayza is less so.
He told La Razon: "Let's be serious, he hasn't played for a long time."